The goal of this paper is to broaden the scope of BSM physics. We propose light vector DM candidates with mass regime (\(1~\rm MeV\)  to \(10~\rm GeV\) ). The interaction of DM with SM is leptophilic and DM particles only interact with SM leptons via spinor mediators. Scattering of vector DM from electron could be consistent with XENON1T [1]} experiment bounds for DM-electron direct detection. The leptophilic models are particularly interesting when we look at the anomalous magnetic moment of the leptons. In this way, we attempt to find out parameter space of the model to explain the newest muon magnetic moment anomaly.
